GEOSTATS: Boundary delimiter algorithm!

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• Hello to everyone! I am trying to delimit a boundary out of a disperse set of points considering only the most external ones. The example should be something
Message 1 of 4 , Feb 6 11:37 PM
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Hello to everyone!

I am trying to delimit a boundary out of a disperse set of points
considering only the most external ones.
The example should be something like the following,

+ +
+
+ +
+
+ +

This are the disperse points

The algorithm will delimited the outside boundary.

+-----+
/ + \
/ + +
+ |
\__ +____+

At the moment we have been triangulating the points and obtaining the
outline, however we are interested in an algorithm which would
recognize the most external points of the area and use them to
create a boundary polygon.

Any help on this, useful web pages or literature would be appreciated.

Paloma Urbano
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• The key word in this problem is convex hull That is the polygon that bounds all points. Shamos and Preparata have algorithms to determine the convex hull.
Message 2 of 4 , Feb 7 8:17 AM
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The key word in this problem is "convex hull" That is the polygon that
bounds all points. Shamos and Preparata have algorithms to determine the
convex hull.

Charlie Hendricksen veritas@...

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• Check out the bottom of http://www.sfiltd.com/products.htm The Convex Hull Generator creates the polygon which you would get if each datapoint were a nail in
Message 3 of 4 , Feb 7 10:44 AM
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Check out the bottom of

http://www.sfiltd.com/products.htm

"The Convex Hull Generator creates the polygon which you would get if each
datapoint were a nail in a board and youstretched a rubber band around the
outside of all of them. "

This is a MapInfo-based solution.

Margie

On Fri, 7 Feb 1997, Paloma Urbano Lopez de Meneses wrote:

> Hello to everyone!
>
>
> I am trying to delimit a boundary out of a disperse set of points
> considering only the most external ones.
> The example should be something like the following,
>
> + +
> +
> + +
> +
> + +
>
> This are the disperse points
>
> The algorithm will delimited the outside boundary.
>
> +-----+
> / + \
> / + +
> + |
> \__ +____+
>

_________________________________________________________
Marjorie Roswell, Spatial Analyst
UMBC Center for Health Program Development and Management
1000 Hilltop Circle Fx: (410)455-6850
Baltimore, MD 21250 E: roswell@...
Ph: (410)455-6802 http://umbc.edu/~roswell/mipage.html
_________________________________________________________

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• ... Dear Paloma, I cannot help you about generic algorithms you ask for, but I suggest you to make sound use of: a) the phisical meaning of the boundary
Message 4 of 4 , Feb 7 4:45 PM
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paloma@... wrote:
>
> Hello to everyone!
>
> I am trying to delimit a boundary out of a disperse set of points
> considering only the most external ones.
> The example should be something like the following,
>
> + +
> +
> + +
> +
> + +
>
> This are the disperse points
>
> The algorithm will delimited the outside boundary.
>
> +-----+
> / + \
> / + +
> + |
> \__ +____+
>
> At the moment we have been triangulating the points and obtaining the
> outline, however we are interested in an algorithm which would
> recognize the most external points of the area and use them to
> create a boundary polygon.
>
> Any help on this, useful web pages or literature would be appreciated.
>
>
> Paloma Urbano

Dear Paloma,

you to make sound use of:
a) the phisical meaning of the boundary polygon that you are looking for;
b) the nature of data linked to the locations.
In effect in many cases you could get good results by just exploiting the tools
of geostatistics (of course used properly) and the selection criteria.
For example, if in each point you have a thickness value of a geological body
and you are looking for an evaluation of the total volume, you could make a
kriging of the thickness at the nodes of a grid superimposed to the potential
interest area.
The boundary could then be defined on the base of the selection made on
kriged values at the grid nodes. You just have to adopt one (or more) sound
criteria :
- a cut off value on the estimation variance (absolute or relative);
- a selection of nodes with a consistent probability of having a positive
thickness, but considering a lower limit of a confidence interval
[Z*- k sigma2(Z*->Z), k>=0.];
- the range value of variogram model of the variable at hand;
- ... and so on, depending on the nature of your problem (a "noise level" is
a variable quite different from "thickness" or from a "proportion", and so is
the associated problem).

Even if you have not the actual values of your (regionalized) variable,
in my opinion you should refer to the true nature of your problem in choosing the
boundarying procedure.

I suggest you to address a specific/technical literature of your working field,
and to examine not a "blind" or generic procedure, but that one which you
select as the most proper when looking at the heart of your problem.

Best regards.

Prof. Roberto BRUNO
Dip. Chemical, Mining & Environmental Technlogies Engineering
Univ. of BOLOGNA, Italy
Tel.(+39-51) 6443393; fax (+39-51) 6443392
E-mail: SCIENMIN2@...
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